Abstract Recently, Gross, Mansour and Tucker introduced the partial-dual polynomial of a ribbon graph as generating function that enumerates all partial duals by Euler genus. It is analogous to extensively studied in topological theory genus embeddings given graph. To investigate polynomial, one only needs focus on bouquets: is, graphs with exactly vertex. In this paper, we shall further show b...

We give a tight bound for the triple intersection numbers of Paley graphs. In particular, we show that any three vertices have common neighbor in graphs order larger than 25.

Abstract Let F be a set of n objects in the plane and let $$\mathcal {G}^{\times }(F)$$ G × ( F ) its intersection graph. A balanced clique-based separator is {\mathcal {S}}$$ S c...